影子价格与影子成本

145Vol.14,No.5200510OPERATIONSRESEARCHANDMANAGEMENTSCIENCEOct.2005:2005201228:(2005sk105):(19572),,,,,,:(,233041):,,,:;;;;;;;:O22111:A:100723221(2005)0520041205ShadowPriceandShadowCostYANGGui2yuan(InstituteofQuantitativeEconomics,AnhuiUniversityofFinance&Economics,Bengbu233041,China)Abstract:Thisarticleconcernstheshadowcostconceptanddiscussestherelationshipbetweenshadowcostanddualpriceaccordingtolinearprogrammingseconomicmeaningofdualvariableandshadowprice.Itgivesadynamicindicationofshadowcostthroughtheanalysisofthesensitivity,andfurtherclarifiestheuniquenessofshadowpriceandshadowcostandtheapplicationofthepatterintheeconomicmanagement.Keywords:operationsresearch;shadowcost;linearprogramming;duallinearprogramming;shadowprice;marginalcost;marginalbenefit;uniqueness0:maxZ=CX(LP1)s.tAXFbXE0C=(c1,c2,,cn),A=(aij)mn,b=(b1,b2,,bm)T,X=(x1,x2,,xn)T,A,C,b(LP1)B,XB=B-1b,XN=0,maxZ=CBB-1b:minW=Yb(DLP1)s.tYAECYE0Y=(y1,y2,,ym),(DLP1)Y3=(y31,y32,,y3m)(LP1)BY3=CBB-1,minW=Y3b=CBB-1b=maxZy3i(i=1,2,,m)i(ShadowPrice)Z=CBB-1b5Z5b=Zb=CBB-1=(y31,y32,,y3m)y31,y32,,y3m:(B),;5Z5bi=y3i(i=1,2,,m)(B),iZibi5Zbi(i=1,2,,m),(marginalprice),i(i=1,2,,m):i(i=1,2,,m),1nm(),m()b=(b1,b2,,bm)T,nC=(c1,c2,,cn),nmA=(aij)mn(i=1,2,,m;j=1,2,,n),nX=(x1,x2,,xn)T,,S:minS=CX(LP2)s.tAXEbXE0:maxG=Yb(DLP2)s.tYAFCYE0Y=(y1,y2,,ym)[1],(DLP2)(LP2)()(marginalcosts)(shadowcosts),iGibiyi=Gbi(i=1,2,,m):(),,(),,,322442,(%)1,,?242005141()3%30%015%325%020%10%2414%007%42(/)0.281.050.70.91x1,x2,x3,x4,:minS=0.28x1+1.05x2+0.7x3+0.91x4(LP3)s.t0103x1+0.3x2+0.15x4E320.05x1+012x3+0.1x4E240114x1+0107x4E42x1,x2,x3,x4E0LINDO6.11,:x1=480,x2=58.67,x3=0,x4=0,minZ=196:480,58.67,,,,196/,,??y1,y2,y3,:maxG=32y1+24y2+42y3(DLP3)s.t0103y1+0.05y2+0.14y3F0.280.3y1F1.050.2y2F0.70.15y1+0.1y2+0.07y3F0.91y1,y2,y3F0(DLP3)(LP3)LINDO6.1(DLP3),:y1=3.5,y2=3.5,y3=0,maxG=196LINDO6.11,(dualprice)-3.5,-3.50,(LP3)(DLP3)y1,y2,y3,1(1),,,1,3.5;1,3.5;1,,67.2423.53.50(marginalcosts)(shadowcosts)[2](LP3),(DLP3)y1=3.5,y2=3.5,y3=02,,(),,b1,y1b1(LP3),LINDO6.1b1345:,y1b1:y1=00b1F93.59b1+(LP3),LINDO6.1b2,y2b2:y2=00b2F153.515b2+(LP3),LINDO6.1b3,y3b3:y3=00b3F67.21.2567.2b3F14913214913b3+,,,,,,,,,;,3,,(),,,,bi,yi,,(LP3),:0Fb1F9,y1=0;9Fb1+,y1=3.5,,b1=9,y1=0y1=3.5,,b1=9b1Z,b1:0Fb19b1=903.5[3,4](LP1)(LP2),(DLP1)(DLP2),,[3,4][5],[5],,:,,(),bi,bibi,,yibi,yi=yi(bi)(i=1,2,,m)():,(),bi,bibi,,yibiyi=yi(bi)(i=1,2,,m),44200514[3]y1,y2,y3,b1=12,b2=8,b3=16,[3]:y1=320Fb1616Fb1101210Fb1120b1E12y2=20Fb24324Fb2818Fb290b2E9y3=120Fb38188Fb3160b3E16y4=340Fb480b4E8,[4],[4]:y1=20Fb14134Fb150b1E5y2=560Fb28238Fb2100b2E104,,,,;,,,,,;,,,,,,,;,,,:[1],.[J].,2000,29(5):5402544.[2].[M].:,2001.18231.[3],.[J].,1999,6:8210.[4].[J].,2001,10(2):33236.[5],,.[J].,2002,11(1):23227.[6],,.[M].:,1998.32268.[7].[J].(),2000,27(2):1102113.[8].[J].,2001,20(2):27229.545: